Manchester City players are queueing up to say Saturday's potentially decisive visit to Goodison cannot be taken for granted, with Everton needing a win to keep their slim top-four hopes alive, though a glance at the table and the fixture list suggests the chances of denying Arsenal a Champions League place moved from slim to malnourished after the calamitous defeats at Crystal Palace and Southampton.

Four points ahead with two games to play, Arsenal need one win from West Bromwich Albion at home this Sunday or Norwich away a week later, while Everton will have to beat both City and Hull away and somehow hope the Gunners trip up twice against relegation-threatened opponents. Arsenal have put together three straight wins since the 3-0 defeat at Goodison that encouraged Everton to keep believing; Roberto Martínez's team have lost twice in the same period and too much ground has surely been lost.

With Aaron Ramsey back and Mesut Özil enjoying himself again, it is hard to see Arsenal letting this opportunity slip. They could put the issue to bed as early as Sunday lunchtime against a West Brom side who still need a point or two to be sure of safety but who have two easier fixtures (Sunderland and Stoke) to come after the Emirates.

Everton will know that, and though the atmosphere at Goodison should still be raucous and City will not be given anything as a present, that will have more to do with it being the final home game of a memorable season than the possibility of ending up in the Champions League. Other considerations to factor in to the equation are that Gareth Barry will have to sit out the game against his parent club, and the most likely beneficiaries of Everton denying City a victory would be Liverpool, who would then go to Crystal Palace on Monday with a chance of putting their title challenge back on track. So one way or the other it is bound to be an interesting day on Merseyside.

You would have to say, with nothing sorted out at the end of April except that Southampton are certain to finish eighth, that it has been a more than usually interesting season. Anything is still possible at the top of the table, where a mere three points separate the top three clubs, and the situation is just as fluid at the bottom, where there are only two points between the bottom four clubs and a win for any of them would have Aston Villa and West Brom looking anxiously over their shoulders.

All the top five clubs still have the same manager with which they started the season, while five of the bottom six have made changes, in Fulham's case multiple changes, though perhaps that only indicates that underperformance makes owners and chairmen nervous. Manchester United kept faith with an underperforming manager for most of the season, and look where that got them. Newcastle United too are currently a very poor advertisement for sticking with the same manager through thick and thin, yet even though Tottenham took a risk by replacing André Villas-Boas with the inexperienced Tim Sherwood, their league form and position has held up remarkably well.

Spurs' last two league games (away to West Ham, then home to Villa) appear more winnable than Everton's last two, so it is not inconceivable that Sherwood could still guide Spurs to a creditable fifth place. Not enough to keep his job, in all probability, with Spurs reportedly talking to Ajax's Frank de Boer, though an achievement that would put Martínez's "fantastic" season at Everton into a more sober perspective.

Martínez, before anyone else points it out, did not have £86m of Gareth Bale money to invest at the start of the season and had to do what he could instead with the cash received for Marouane Fellaini on the final day. He did not do too badly, buying James McCarthy from Wigan, bringing in Romelu Lukaku, Gerard Deulofeu and Barry on loan and successfully switching Everton on to a more possession-based game. It was not Martínez either who promised Champions League football, that was Bill Kenwright rather ill-advisedly revealing the contents of a private conversation and creating a rod for his new manager's back in his first season. Martínez probably could get Everton into the Champions League bracket eventually, but for the annoying habit other leading clubs have developed of ploughing tens of millions into the same project. If everyone could stand still for a couple of seasons, Everton might rise above fifth place based on the quality of their football and their manager's relentless positivity.

Unfortunately, football doesn't work quite like that, and the harsh reality is that should Everton miss out this season, with Manchester United nowhere, it may take them a while to get as close again. United will have a new manager next season, and by all accounts will be investing massively over summer. It might not have the desired effect – something similar was being mooted this time last year – but whether Ryan Giggs or Louis van Gaal is in charge it seems unlikely, given the transfer budget and targets being talked about, that United will finish as low as seventh again.

Arsenal, Liverpool and Tottenham will also be strengthening over the summer, perhaps not to the same extent but in all likelihood to a greater extent than Everton, and if Liverpool are to return to being a fixture in the top four it is hard to see how their neighbours can also squeeze in. Under present ownership and management Chelsea and Manchester City are unlikely to drop out of the Champions League elite, so that leaves Arsenal, Liverpool, Spurs and United battling with Everton for the remaining two places. This season, with United struggling, Spurs stuttering and Arsenal looking unconvincing much of the time, represented a rare opportunity for Everton, but how many times in the foreseeable future are those conditions likely to be repeated?

Yet while Everton still have a slim to malnourished chance of a top-four place this season it would be wrong to write them off, or underestimate the sense of adventure and belief Martínez has brought to Merseyside. It is typical of Everton's luck that when they finally found a manager who could do that, Liverpool found one too. Everton's performances home and away against Arsenal were probably the high points, given that the excitement of winning at Old Trafford subsided slightly when it became clear that almost anyone could do it, though the league table can confirm that overall improvement this season has been real and not imagined.

Last season Everton finished in sixth place with 63 points. Right now they are fifth, on 69, with two games to play. Winning both those games might not be enough to take them into the Champions League, because Arsenal are four points ahead. But should Everton win them they would end up on 75 points, which is as many as Chelsea took to finish third last season.

Should Everton take four points from their next two games they would finish on 73, which was good enough to see Arsenal finish fourth last season. This season it might not be enough, the bar for Champions League qualification could be set as high as 79, but no one could possibly deny that Everton under Martínez have raised their own bar significantly. Small margins, Martínez is fond of saying, are what make the difference in football. Everton are close, yet not quite close enough. Small margins may continue to confound them for some time.